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Theorems · Definition · general topology

Dilation.comp

{α : Type u_1} →
  {β : Type u_2} →
    {γ : Type u_3} →
      [inst : PseudoEMetricSpace α] →
        [inst_1 : PseudoEMetricSpace β] → [inst_2 : PseudoEMetricSpace γ] → β →ᵈ γ → α →ᵈ β → α →ᵈ γ

The composition of dilations is a dilation

Defined in
Mathlib.Topology.MetricSpace.Dilation
Cited by
10 results in Mathlib
Foundations
Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpacePseudoEMetricSpacePseudoEMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DilationEquiv.trans · cited by 7DilationEquiv.transDilation.ratio_comp' · cited by 3Dilation.ratio_comp'Dilation.comp_apply · cited by 1Dilation.comp_applyDilation.mul_def · cited by 0Dilation.mul_defDilation.cancel_left · cited by 0Dilation.cancel_leftDilation.cancel_right · cited by 0Dilation.cancel_rightDilation.id_comp · cited by 0Dilation.id_compDilation.coe_comp · cited by 0Dilation.coe_compDilation.ratio_comp · cited by 0Dilation.ratio_compDilation.comp_assoc · cited by 0Dilation.comp_assocDilation.comp_id · cited by 0Dilation.comp_idDFunLike.coe · cited by 62936DFunLike.coePseudoEMetricSpace · cited by 1536PseudoEMetricSpaceDilation · cited by 44DilationDilation.compCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.